Question

Write the value of $(\frac{x^a}{x^b}{)}^{a+b}\times (\frac{x^b}{x^c}{)}^{b+c}\times (\frac{x^c}{x^a}{)}^{c+a}$

Answer 1

As we know that

$\frac{a^m}{a^n}=a^{m-n}$ and also $(a+b)(a-b)=a^2-b^2$

$(\frac{x^a}{x^b}{)}^{a+b}\times (\frac{x^b}{x^c}{)}^{b+c}\times (\frac{x^c}{x^a}{)}^{c+a}=(x^{a-b}{)}^{a+b}\times (x^{b-c}{)}^{b+c}\times (x^{c-a}{)}^{c+a}=x^{a^2-b^2}\times x^{b^2-c^2}\times x^{c^2-a^2}=x^{a^2-b^2+b^2-c^2+c^2-a^2}=x^0=1$